Problem: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-5x-3y &= -4 \\ -6x-2y &= -3\end{align*}$
Begin by moving the $x$ -term in the second equation to the right side of the equation. $-2y = 6x-3$ Divide both sides by $-2$ to isolate $y$ $y = {-3x + \dfrac{3}{2}}$ Substitute this expression for $y$ in the first equation. $-5x-3({-3x + \dfrac{3}{2}}) = -4$ $-5x + 9x - \dfrac{9}{2} = -4$ Simplify by combining terms, then solve for $x$ $4x - \dfrac{9}{2} = -4$ $4x = \dfrac{1}{2}$ $x = \dfrac{1}{8}$ Substitute $\dfrac{1}{8}$ for $x$ back into the top equation. $-5( \dfrac{1}{8})-3y = -4$ $-\dfrac{5}{8}-3y = -4$ $-3y = -\dfrac{27}{8}$ $y = \dfrac{9}{8}$ The solution is $\enspace x = \dfrac{1}{8}, \enspace y = \dfrac{9}{8}$.